Cover Image

Calculus for Dummies.

Bibliographic Details
Main Author: Ryan, Mark.
Format: eBook
Language:English
Published: New York : John Wiley & Sons, Incorporated, 2016.
Edition:2nd ed.
Subjects:
Calculus.
Electronic books.
Online Access:View fulltext via EzAccess
Table of Contents:
  • Intro
  • Title Page
  • Copyright Page
  • Table of Contents
  • Introduction
  • About This Book
  • Foolish Assumptions
  • Icons Used in This Book
  • Beyond the Book
  • Where to Go from Here
  • Part 1 An Overview of Calculus
  • Chapter 1 What Is Calculus?
  • What Calculus Is Not
  • So What Is Calculus, Already?
  • Real-World Examples of Calculus
  • Chapter 2 The Two Big Ideas of Calculus: Differentiation and Integration - plus Infinite Series
  • Defining Differentiation
  • The derivative is a slope
  • The derivative is a rate
  • Investigating Integration
  • Sorting Out Infinite Series
  • Divergent series
  • Convergent series
  • Chapter 3 Why Calculus Works
  • The Limit Concept: A Mathematical Microscope
  • What Happens When You Zoom In
  • Two Caveats
  • or, Precision, Preschmidgen
  • I may lose my license to practice mathematics
  • What the heck does "infinity" really mean?
  • Part 2 Warming Up with Calculus Prerequisites
  • Chapter 4 Pre-Algebra and Algebra Review
  • Fine-Tuning Your Fractions
  • Some quick rules
  • Multiplying fractions
  • Dividing fractions
  • Adding fractions
  • Subtracting fractions
  • Canceling in fractions
  • Absolute Value - Absolutely Easy
  • Empowering Your Powers
  • Rooting for Roots
  • Roots rule - make that, root rules
  • Simplifying roots
  • Logarithms - This Is Not an Event at a Lumberjack Competition
  • Factoring Schmactoring - When Am I Ever Going to Need It?
  • Pulling out the GCF
  • Looking for a pattern
  • Trying some trinomial factoring
  • Solving Quadratic Equations
  • Method 1: Factoring
  • Method 2: The quadratic formula
  • Method 3: Completing the square
  • Chapter 5 Funky Functions and Their Groovy Graphs
  • What Is a Function?
  • The defining characteristic of a function
  • Independent and dependent variables
  • Function notation
  • Composite functions
  • What Does a Function Look Like?.
  • Common Functions and Their Graphs
  • Lines in the plane in plain English
  • Parabolic and absolute value functions - even steven
  • A couple oddball functions
  • Exponential functions
  • Logarithmic functions
  • Inverse Functions
  • Shifts, Reflections, Stretches, and Shrinks
  • Horizontal transformations
  • Vertical transformations
  • Chapter 6 The Trig Tango
  • Studying Trig at Camp SohCahToa
  • Two Special Right Triangles
  • The 45°-45°-90° triangle
  • The 30°-60°-90° triangle
  • Circling the Enemy with the Unit Circle
  • Angles in the unit circle
  • Measuring angles with radians
  • Honey, I shrunk the hypotenuse
  • Putting it all together
  • Graphing Sine, Cosine, and Tangent
  • Inverse Trig Functions
  • Identifying with Trig Identities
  • Part 3 Limits
  • Chapter 7 Limits and Continuity
  • Take It to the Limit - NOT
  • Using three functions to illustrate the same limit
  • Sidling up to one-sided limits
  • The formal definition of a limit - just what you've been waiting for
  • Limits and vertical asymptotes
  • Limits and horizontal asymptotes
  • Calculating instantaneous speed with limits
  • Linking Limits and Continuity
  • Continuity and limits usually go hand in hand
  • The hole exception tells the whole story
  • Sorting out the mathematical mumbo jumbo of continuity
  • The 33333 Limit Mnemonic
  • Chapter 8 Evaluating Limits
  • Easy Limits
  • Limits to memorize
  • Plugging and chugging
  • The "Real Deal" Limit Problems
  • Figuring a limit with your calculator
  • Solving limit problems with algebra
  • Take a break and make yourself a limit sandwich
  • Evaluating Limits at Infinity
  • Limits at infinity and horizontal asymptotes
  • Solving limits at infinity with a calculator
  • Solving limits at infinity with algebra
  • Part 4 Differentiation
  • Chapter 9 Differentiation Orientation
  • Differentiating: It's Just Finding the Slope.
  • The slope of a line
  • The derivative of a line
  • The Derivative: It's Just a Rate
  • Calculus on the playground
  • Speed - the most familiar rate
  • The rate-slope connection
  • The Derivative of a Curve
  • The Difference Quotient
  • Average Rate and Instantaneous Rate
  • To Be or Not to Be? Three Cases Where the Derivative Does Not Exist
  • Chapter 10 Differentiation Rules - Yeah, Man, It Rules
  • Basic Differentiation Rules
  • The constant rule
  • The power rule
  • The constant multiple rule
  • The sum rule - hey, that's some rule you got there
  • The difference rule - it makes no difference
  • Differentiating trig functions
  • Differentiating exponential and logarithmic functions
  • Differentiation Rules for Experts - Oh, Yeah, I'm a Calculus Wonk
  • The product rule
  • The quotient rule
  • The chain rule
  • Differentiating Implicitly
  • Getting into the Rhythm with Logarithmic Differentiation
  • Differentiating Inverse Functions
  • Scaling the Heights of Higher Order Derivatives
  • Chapter 11 Differentiation and the Shape of Curves
  • Taking a Calculus Road Trip
  • Climb every mountain, ford every stream: Positive and negative slopes
  • I can't think of a travel metaphor for this section: Concavity and inflection points
  • This vale of tears: A local minimum
  • A scenic overlook: The absolute maximum
  • Car trouble: Teetering on the corner
  • It's all downhill from here
  • Your travel diary
  • Finding Local Extrema - My Ma, She's Like, Totally Extreme
  • Cranking out the critical numbers
  • The first derivative test
  • The second derivative test - no, no, anything but another test!
  • Finding Absolute Extrema on a Closed Interval
  • Finding Absolute Extrema over a Function's Entire Domain
  • Locating Concavity and Inflection Points
  • Looking at Graphs of Derivatives Till They Derive You Crazy
  • The Mean Value Theorem - GRRRRR.
  • Chapter 12 Your Problems Are Solved: Differentiation to the Rescue!
  • Getting the Most (or Least) Out of Life: Optimization Problems
  • The maximum volume of a box
  • The maximum area of a corral - yeehaw!
  • Yo-Yo a Go-Go: Position, Velocity, and Acceleration
  • Velocity, speed, and acceleration
  • Maximum and minimum height
  • Velocity and displacement
  • Speed and distance traveled
  • Burning some rubber with acceleration
  • Tying it all together
  • Related Rates - They Rate, Relatively
  • Blowing up a balloon
  • Filling up a trough
  • Fasten your seat belt: You're approaching a calculus crossroads
  • Chapter 13 More Differentiation Problems: Going Off on a Tangent
  • Tangents and Normals: Joined at the Hip
  • The tangent line problem
  • The normal line problem
  • Straight Shooting with Linear Approximations
  • Business and Economics Problems
  • Managing marginals in economics
  • Part 5 Integration and Infinite Series
  • Chapter 14 Intro to Integration and Approximating Area
  • Integration: Just Fancy Addition
  • Finding the Area Under a Curve
  • Approximating Area
  • Approximating area with left sums
  • Approximating area with right sums
  • Approximating area with midpoint sums
  • Getting Fancy with Summation Notation
  • Summing up the basics
  • Writing Riemann sums with sigma notation
  • Finding Exact Area with the Definite Integral
  • Approximating Area with the Trapezoid Rule and Simpson's Rule
  • The trapezoid rule
  • Simpson's rule - that's Thomas (1710-1761), not Homer (1987-)
  • Chapter 15 Integration: It's Backwards Differentiation
  • Antidifferentiation
  • Vocabulary, Voshmabulary: What Difference Does It Make?
  • The Annoying Area Function
  • The Power and the Glory of the Fundamental Theorem of Calculus
  • The Fundamental Theorem of Calculus: Take Two
  • Why the theorem works: Area functions explanation.
  • Why the theorem works: The integration-differentiation connection
  • Why the theorem works: A connection to - egad! - statistics
  • Finding Antiderivatives: Three Basic Techniques
  • Reverse rules for antiderivatives
  • Guessing and checking
  • The substitution method
  • Finding Area with Substitution Problems
  • Chapter 16 Integration Techniques for Experts
  • Integration by Parts: Divide and Conquer
  • Picking your u
  • Integration by parts: Second time, same as the first
  • Tricky Trig Integrals
  • Integrals containing sines and cosines
  • Integrals containing secants and tangents or cosecants and cotangents
  • Your Worst Nightmare: Trigonometric Substitution
  • Case 1: Tangents
  • Case 2: Sines
  • Case 3: Secants
  • The As, Bs, and Cxs of Partial Fractions
  • Case 1: The denominator contains only linear factors
  • Case 2: The denominator contains irreducible quadratic factors
  • Bonus: Equating coefficients of like terms
  • Chapter 17 Forget Dr. Phil: Use the Integral to Solve Problems
  • The Mean Value Theorem for Integrals and Average Value
  • The Area between Two Curves - Double the Fun
  • Finding the Volumes of Weird Solids
  • The meat-slicer method
  • The disk method
  • The Washer Method
  • The matryoshka-doll method
  • Analyzing Arc Length
  • Surfaces of Revolution - Pass the Bottle 'Round
  • Chapter 18 Taming the Infinite with Improper Integrals
  • L'Hôpital's Rule: Calculus for the Sick
  • Getting unacceptable forms into shape
  • Improper Integrals: Just Look at the Way That Integral Is Holding Its Fork!
  • Improper integrals with vertical asymptotes
  • Improper integrals with one or two infinite limits of integration
  • Blowing Gabriel's horn
  • Chapter 19 Infinite Series
  • Sequences and Series: What They're All About
  • Stringing sequences
  • Summing series
  • Convergence or Divergence? That Is the Question.
  • A no-brainer divergence test: The nth term test.

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